With the recent release of Sgt. Bowe Bergdahl from Taliban captivity after nearly five years--in exchange for five mid- to high-level Afghan Taliban figures--criticism immediately emerged questioning not only how the deal suddenly came about but also whether dealing with the Taliban could set a dangerous precedent for U.S. national security.

“This is a complete change of our national security strategy of not negotiating with terrorists,” Rep. Mike Rogers, R-Michigan, told ABC News Monday. “I think it sends a terrible national security message – not just to Afghanistan, but to the rest of the world.”

But did President Obama’s White House, through the Qatari government which brokered the deal, negotiate with terrorists, as suggested by Rogers and a number of high-profile Republicans?

When asked Monday if the White House considered the Taliban terrorists, Press Secretary Jay Carney dodged.

“We don’t get to choose our enemies when we go to war,” Carney told reporters. “We regard the Taliban as an enemy combatant in a conflict that has been going on, in which the United States has been involved for more than a decade. In this case--as you know we dealt with the Qataris in order to secure [Bergdahl’s] release--it was absolutely the right thing to do.”

But Tuesday White House National Security Council spokesperson Caitlin Hayden noted that the Taliban was added to the list of Specially Designated Global Terrorists (SDGT) by executive order in July 2002, even if it is not listed as a Foreign Terrorist Organization (FTO) by the State Department. Either designation triggers asset freezes, according to the State Department, though they can differ on other restrictions imposed on the target organization. The Treasury Department told ABC News the Taliban is still on their SDGT list.

The U.S. is offering $10 million for information leading to the capture of the Taliban's leader, Mullah Omar, through the State Department’s Rewards for Justice program, an effort designed to “fight against international terrorism.” The National Counterterrorism Center also lists “Taliban Presence in Afghanistan” on its global map of “Terrorist Groups.”

Though the State Department has not designated the Afghan Taliban as an FTO, it has designated the group’s sister network, the Pakistani Taliban, as well as the Haqqani Network, a group closely associated with the Taliban that was believed to have been actually holding Bergdahl for most of his captivity. Hayden told ABC News the U.S. “did not negotiate with the Haqqanis” for Bergdahl.

Rather than arguing the status of the Taliban, however, the administration has launched a coordinated effort to characterize Bergdahl as a prisoner of war, rather than a hostage.

“Sgt. Bergdahl was not a hostage, he was a member of the military who was detained during the course of an armed conflict,” Hayden said. “The United States does not leave a soldier behind based on the identity of the party to the conflict... It was a prisoner exchange. We’ve always done that across many wars. With the Germans. The Japanese. The North Koreans.”

As President Obama put it earlier Tuesday, “This is what happens at the end of wars.”

The logic hasn’t convinced some of the president’s biggest critics across the aisle.